if x is not an integer
asked Aug 27, 2014 in Other Math Topics by jeshlin (160 points)

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To prove convergence, if we can show that the terms in the given infinite series are smaller than the terms in an infinite series known to converge then the series must be convergent. In the question we can take pairs of consecutive terms and perform such a comparison. If we take x=0, the series becomes (1/2 - 1/12) + (1/30 - 1/56) +... These pairs of terms can each be treated as one term because the series is infinite. Each such term is less than 1/2 of the term preceding it and we know that the series 1/2+1/4+1/8+1/16+... converges to 1. So the given series must converge.

answered Sep 28, 2014 by Rod Top Rated User (487,100 points)
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